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Development of Hourly Meteorological Values From Daily Data and Significance to
Hydrological Modeling at H. J. Andrews Experimental Forest
SCOTT R. WAICHLER
AND
MARK S. WIGMOSTA
Pacific Northwest National Laboratory, Richland, Washington
(Manuscript received 22 May 2002, in final form 20 September 2002)
ABSTRACT
Hydrologic modeling depends on having quality meteorological input available at the simulation time step.
Often two needs arise: disaggregation from daily to subdaily and extend an available subdaily record. Simple
techniques were tested for generating hourly air temperature, precipitation, solar radiation, relative humidity,
and wind speed from limited daily data at the H. J. Andrews Experimental Forest, Oregon. Skill of the daily to
hourly methods ranged from poor to very good. The best method for each variable had mean error ,4% and
first-degree efficiency .0.5, with the exception of wind speed, which had a bias problem related to change in
measurement height. Significance of the disaggregation assumptions for simulated hydrology was evaluated by
driving the Distributed Hydrology Soil Vegetation Model (DHSVM) with alternative meteorological inputs. The
largest differences in streamflow simulation efficiency were related to differences in precipitation phase, which
followed from the air temperature method used. The largest differences in annual water balance were related
to the humidity model used; the common fallback assumption that daily dewpoint temperature equals minimum
air temperature led to sharply higher evapotranspiration. Hourly streamflow and annual water balance were less
sensitive to the method of distributing precipitation throughout the day and parameterization of solar radiation.
1. Introduction
Simulation of hydrological processes at timescales
less than a day requires the hydrologic model to operate
at subdaily time steps and to utilize diurnal variation in
meteorological forcing. For example, the Distributed
Hydrology Soil Vegetation Model (DHSVM; Wigmosta
et al. 1994, 2002) is designed to work best at a timestep
of 3 h or less. Meteorological (hereafter ‘‘met’’) input
for this model consists of air temperature, precipitation,
relative humidity, wind speed, solar radiation, and longwave radiation at the same time step as the output. For
most mountain watersheds only a few daily met variables are readily available at nearby stations: typically,
minimum and maximum air temperature, daily total precipitation, and perhaps humidity. Therefore, use of hydrologic models like DHSVM requires disaggregation
to provide met input at the subdaily time step, and the
estimation of required but unmeasured met variables.
Disaggregation techniques are especially useful for extending a subdaily record to a period of time when only
daily data are available. Previous studies have focused
on generating daily met data at specific sites (Running
et al. 1987) or over large areas (Thornton et al. 1997;
Corresponding author address: Dr. Scott R. Waichler, Pacific
Northwest National Laboratory, K9-36, P.O. Box 999, Richland, WA
99352.
E-mail: scott.waichler@pnl.gov
q 2003 American Meteorological Society
Thornton and Running 1999). This study asks how well
can hourly values be predicted from a few daily variables at a single, relatively data-rich location in the
Oregon Cascades. It also explores the significance of
the met estimation for simulating the hydrology of an
adjacent experimental watershed.
The setting for this study is the H. J. Andrews Experimental Forest (HJA), Oregon (Fig. 1). The cool, wet,
conifer forest of the HJA is one of the longest running
field sites in the Long Term Ecological Research Network (LTER) and has been the subject of much empirical research on the hydrology of steep, forested catchments (e.g., Jones 2000). Local climate is dominated by
frontal systems from the Pacific Ocean during November–May, and by regional high pressure systems producing warm, dry conditions the rest of the year. Average annual precipitation is 2300 mm, and mean temperature is 98C.
A few HJA studies have used process-based modeling
as the primary method of investigation (e.g., Tague and
Band 2001a,b), but none have focused on meteorological modeling and its relationship to hydrologic predictions. The meteorology measurement program at HJA
(Henshaw et al. 1998; Bierlmaier and McKee 1989)
includes hourly observations since the 1970s and provides a rich opportunity for the development and verification of local meteorology models. We focused on
the two met stations closest to the small watershed WS2
and first addressed the question of how well daily data
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lock forest. To evaluate the significance of the hourly
meteorological synthesis for hydrologic predictions, 14
sets of met input representing different levels of quality
and met modeling assumptions were used to drive
DHSVM and simulate the hydrology of WS2 during
water years 1980–98 (WY80–98).
2. Hourly meteorological modeling
FIG. 1. H. J. Andrews Experimental Forest, showing locations of
small watersheds WS1–3, and climate stations PRIMET and
CS2MET.
could be used to estimate subdaily values. WS2 is 0.6
km 2 in area, and has an elevation range of 450–1000
m, placing it in the rain–snow transition zone. WS2 has
served as a control watershed during a paired watershed
study that began in the late 1950s, and its vegetation
has remained an old-growth Douglas fir–Western hem-
Climate data were obtained from the primary met
station (PRIMET) and another station located adjacent
to WS2 (CS2MET; Fig. 1) (Henshaw et al. 1998). PRIMET is located at 430-m elevation in a valley-bottom
clearing. The valley bottom is approximately 200-m
wide and is subject to early morning and late afternoon
topographic shading. CS2MET is located at 485-m elevation in a smaller clearing within the forest and is
subject to shading from both canopy and topography.
Hourly met values for WY80–98 were estimated from
daily PRIMET data using common disaggregation and
estimation techniques (Table 1), and compared to the
hourly observations. Hourly met values at PRIMET
were also estimated from daily CS2MET data, because
CS2MET has a longer record and is needed for hydrologic modeling prior to 1979.
Daily minimum air temperature (Tmin ), maximum air
temperature (Tmax ), precipitation (P d ), minimum relative
humidity (Hmin ), maximum relative humidity (Hmax ), and
mean wind speed (W d ) were used to predict hourly values of air temperature (T), precipitation (P), relative
humidity (H), wind speed (W), and shortwave solar radiation (R s ) at PRIMET. Hourly data from WY80–89
were used to calibrate the disaggregation methods, and
data from WY90–98 were used for verification. No data
for longwave radiation were available, so we used without verification the method of Bras (1990) and Bowling
and Lettenmaier (1997), which is based on hourly air
temperature, relative humidity, and daily atmospheric
transmittance. Model skill at reproducing the hourly
data was quantified with a bias measure and three in-
TABLE 1. Daily to hourly disaggregation and estimation methods for meteorological variables. Calibration 5 yes means prior inspection
or calculation using some hourly data is involved.
Model
Parameter
1a
1b
1c
2a
2b
3a
3b
3c
4a
4b
4c
4d
4e
5a
5b
Air temperature
Air temperature
Air temperature
Precipitation
Precipitation
Atmospheric transmittance
Atmospheric transmittance
Atmospheric transmittance
Relative humidity
Relative humidity
Relative humidity
Relative humidity
Relative humidity
Wind speed
Wind speed
Description
Modified sine curve
Modified sine curve and 2-h shift
[month, hour, precip] means
1/24th daily total
Relative [month, hour] fraction 3 daily total
BC model with their Pacific Northwest parameters
Bristow–Campbell model with HJA parameters
[month, precip] means
Tdew 5 Tmin
Tdew 5 aTmin 1 b
Hmin, Hmax, Eq. (4)
Hmin,Hmax, Eq. (4), and 2-h shift
[month, hour, precip] means
Daily mean
[month, hour, precip] means
Calibration
no
yes
yes
no
yes
no
yes
yes
no
yes
no
yes
yes
no
yes
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WAICHLER AND WIGMOSTA
creasingly stringent tests of efficiency (see appendix for
definitions of efficiency statistics). Bias was defined as
P /O , where P is mean of simulated values and O is
mean of observed values.
Two types of categorical means and bias corrections
were used in the modeling of hourly met values, with
domain defined by categorical factors denoted with
square brackets. The first type used month and hour
[month, hour] factors; the second used those factors plus
daily precipitation (precip)—status wet or dry [month,
hour, precip]. Categorical means and bias corrections
were computed from data in the hourly meteorological
model calibration period (WY80 –89). Categorical
means were used as another predictor for air temperature, precipitation, atmospheric transmittance, humidity,
and wind speed (methods 1c, 2b, 3c, 4e, 5b, respectively
in Table 1). All methods were used to predict met variables in the calibration period (WY80–89) and verification period (WY90–98). Categorical bias corrections
were used to account for differences between CS2MET
and PRIMET stations when generating met input for the
hydrologic model. The difference between hourly estimated CS2MET and observed PRIMET categorical
means were computed and added to CS2MET hourly
values to get the final, unbiased estimate for the PRIMET location.
a. Air temperature
Hourly values of T were generated by computing a
modified sine curve from daily Tmin and Tmax , following
the method of Running et al. (1987) and Parton and
Logan (1981). Daylight air temperature was modeled
using three quadrants of a sine wave (2p/2 to p) with
the minimum value at sunrise, maximum value at solar
noon (p/2), and mean value at sunset (p). Sunrise and
sunset times were computed with a solar geometry model (Gates 1980; Bowling and Lettenmaier 1997), assuming level ground free from topographic shading. Nighttime air temperature was modeled as a linear interpolation between sunset T of the previous day and sunrise
T of the following day. The modified sine curve approach can be viewed as the minimum viable method
for generating T (method 1a in Table 1). Shifting the
resulting sine curve 2 h earlier yielded the best match
to the observations (method 1b). Another alternative
was to use the [month, hour, precip] categorical means
from the calibration period (method 1c).
To generate hourly air temperature using CS2MET
data, [month, hour, precip] bias corrections were computed from data in the calibration period and added to
the modified sine curve based on CS2MET Tmin and Tmax
to yield the final air temperatures (Fig. 2). For wet days,
the bias correction was 18–28C during the wet season.
Cloud cover associated with wet days reduced nighttime
cooling, producing a smaller range in diurnal temperature. For dry days, a strong diurnal pattern was evident,
with the maximum bias correction (up to 68C) occurring
253
FIG. 2. Bias corrections for CS2MET air temperature. The correction corresponding to a particular [month, hour, precip] combination
was applied after generating hourly values using the modified sine
curve method and applying a 2-h shift. The final time series represented the best unbiased estimate of hourly PRIMET air temperature
from CS2MET daily data.
around midday, and the minimum occurring around
dawn. For comparison, the difference between these stations, according to the mean lapse rate of 24.28C km 21
(Rosentrater 1997), would be only 0.28C. The effect of
location apart from elevation difference indicates the
potential difficulty in spatial interpolation or extrapolation, even over small distances.
The modified sine curve method with a 2-h shift
(method 1b) resulted in the best fit to the observations
(Table 2, Fig. 3). The least successful predictor of air
temperature was the categorical means model (method
1c). Air temperature modeling had the most skill of the
five met variables, with bias close to 1.0 and efficiency
values among the highest obtained. The efficiency statistics have a possible range of 2` to 1.0. A value of
0 indicates the model is no better or worse than the
observed mean as a predictor. Efficiency generally declines from calibration to verification, and from using
a less specific mean to a more specific mean for comparison (e.g., from grand mean to [month, hour, precip]
categorical mean).
b. Precipitation
Two methods were used to predict hourly precipitation P. The first used a uniform distribution of the daily
total, where P 5 P d /24 (method 2a, Table 1). The second
method used relative [month, hour] fractions f m,h , where
24
m is month, h is hour; and S h51
f m,h 5 1 for all m; and
P 5 P d f m,h (method 2b, Table 1). When using CS2MET
daily data, a bias correction factor (50.956) was computed as the ratio of total PRIMET to CS2MET precipitation during WY80–98, and applied to all hourly
simulated values.
Precipitation goodness-of-fit was much lower than for
air temperature, with efficiency ,0.3 (Table 2, Fig. 4).
The relative fractions method was somewhat better than
the uniform distribution, but the difference was small
in this climate with little diurnal pattern in precipitation.
With both methods, observed precipitation values great-
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TABLE 2. Meteorological model skill for T, P, and Tr . Hourly variables except atmospheric transmittance, which is daily. See appendix
for efficiency equations.
Model
Period
Biasa
Air temperature
1a
1b
1c
1a
1b
1c
WY80–89
WY80–89
WY80–89
WY90–98
WY90–98
WY90–98
Precipitation
2a
2b
2a
2b
WY80–89
WY80–89
WY90–98
WY90–98
Atmospheric transmittance
3a
WY80–89
3b
WY80–89
3c
WY80–89
3a
WY90–98
3b
WY90–98
3c
WY90–98
E 1b
E91 c
0.951
0.951
1
0.963
0.963
0.963
0.616
0.788
0.576
0.595
0.785
0.564
0.206
0.561
0.123
0.166
0.557
0.089
0.094
0.5
0
0.06
0.501
20.025
1.013
1.013
1.025
1.025
0.286
0.293
0.276
0.284
0.265
0.272
0.257
0.266
—
—
—
—
20.096
0.506
0.423
0.004
0.525
0.451
20.429
0.356
0.247
20.266
0.397
0.302
1.4450
0.983
1
1.419
1.016
1.002
E01 d
20.879
0.152
0
20.116
0.468
0.385
Ratio of simulated to observed mean.
Efficiency relative to grand mean of observations.
Efficiency relative to [month, hour] categorical mean, except [month] for atmospheric transmittance.
d
Efficiency relative to [month, hour, precip] categorical mean, except [month, precip] for atmospheric transmittance.
a
b
c
er than 6 mm h 21 were underpredicted, and values greater than 10 mm h 21 were underpredicted by 50% or more.
c. Solar radiation
First, atmosphere-incident shortwave solar radiation
R a was calculated from latitude and time of year using
a solar geometry model (Gates 1980). Then the Bristow
and Campbell (1984) model (BC) was used to predict
daily atmospheric transmittance (T r ), and together with
R a , hourly shortwave solar radiation R s at the land surface. The BC model estimates daily atmospheric transmittance from time of year and difference between daily
minimum and maximum temperature,
T r 5 Ap(1 2 e 2BmDT C ),
(1)
where
5 coefficient, equivalent to the maximum atmospheric transmittance,
p 5 coefficient, 1.0 on dry days, ,1.0 on wet
days,
B m 5 coefficient that varies by month,
DT 5 Tmax 2 Tmin ,
C 5 coefficient.
A
Observed T r for each day was assumed to be the mean
of the hourly values from 1200 to 1500 h. This subset
of the day was used to avoid topographic shading effects
in morning and late afternoon. Coefficients in Eq. (1)
were taken from Bristow and Campbell (1984; method
3a) or were calibrated (method 3b). In the latter case,
coefficient A was estimated as the maximum ratio of
observed solar radiation to predicted radiation at the top
of the atmosphere (R s /R a ) during the calibration period,
resulting in A 5 0.73, similar to 0.70 found by Bristow
and Campbell (1984) for Pullman, Washington. Next, p
and C were fitted by trial and error to the nearest 0.01,
and B m for each month was fitted with a nonlinear regression function, using all days in the calibration period. On dry days, p was fixed to 1.0, and a single value
was found for all wet days. The parameter set with the
maximum efficiency E91 value was selected: A 5 0.73,
C 5 0.70, p 5 0.65 (wet days), B m 5 [0.2089 (January),
0.2857, 0.2689, 0.2137, 0.1925, 0.2209, 0.2527, 0.2495,
0.2232, 0.1728, 0.1424, 0.1422 (December)]. Model
skill was evaluated with respect to daily atmospheric
transmittance rather than hourly solar radiation because
of topographic shading at PRIMET. Finally, hourly solar
radiation incident to level ground (R s ) was computed as
Rs 5 Tr Ra .
The BC model calibrated for local conditions (method
3b) was the best method for predicting daily atmospheric transmittance T r (Fig. 5), but efficiency was
much lower than for air temperature or precipitation
(Table 2). It was slightly more efficient than using
[month, hour, precip] means to predict T r . The BC model
with parameter values from Bristow and Campbell
(1984; method 3a) had the lowest efficiency.
d. Humidity
Hourly PRIMET relative humidity prior to 8 July
1988 was not available, so the calibration and verifi-
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WAICHLER AND WIGMOSTA
FIG. 3. Mean hourly temperature by month, verification period (WY90–98). Simulated values from PRIMET daily data, sine curve, and
2-h shift (method 1b, Table 1).
cation periods were shortened to WY89–93 and WY94–
98, respectively. The minimal method (method 4a) for
estimating hourly H assumes that daily minimum air
temperature is the same as dewpoint, Tmin 5 Tdew , then
uses
H5
Vs (Tdew )
,
Vs (T )
(2)
where V s (Tdew ) equals the saturation vapor pressure at
Tdew , and V s (T) equals the saturation vapor pressure at
FIG. 4. Mean hourly precipitation on wet days by month, verification period (WY90–98). Simulated values from mean [month, hour]
fractions 3 daily total P (method 2b, Table 1).
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e. Wind speed
FIG. 5. Daily atmospheric transmittance by month, verification period (WY90–98). Simulated values using Bristow–Campbell coefficients tuned for HJA (method 3b, Table 1).
T. A slightly better approach (Running et al. 1987) uses
a simple linear regression and is feasible if an independent measurement of Tdew is available (method 4b):
Tdew 5 a 0 1 a1 Tmin .
(3)
For WY80–89, a 0 5 1.95 and a1 5 0.938; both terms
were significant (p value , 0.0001; R 2 5 0.88).
Since daily Hmin and Hmax were available, hourly values could also be estimated as (methods 4c, 4d)
H 5 Hmax 1
Hourly meteorological modeling was least successful
for wind speed. The [month, hour, precip] means model
(method 5b) was a better predictor than the mean daily
wind speed (method 5a) during both periods (Table 3).
However, there was significant positive bias in the
WY90–98 verification run of method 5b for most
months, especially around midday (Fig. 7). The 129%
bias in predicted wind speed for WY90–98 may have
been caused in part by a reduction in the measurement
height, which occurred close to the end of the calibration
period. On 1 January 1989 the measurement height was
reduced from 12 to 10 m. We applied a logarithmic wind
profile to see if the height change could account for the
wind speed bias. Applying typical assumptions for the
zero-plane displacement height and momentum roughness parameter, we could only account for a 14% bias.
Measurement factors other than instrument height probably also changed.
(T 2 Tmin )
(H 2 Hmax ).
(Tmax 2 Tmin ) min
(4)
For relative humidity, the only method with efficiency
consistently greater than zero was the [month, hour, precip]
means model (method 4e) (Table 3, Fig. 6). The next best
predictor was Eq. (4) with a 2-h shift (method 4d). Humidity actually had higher efficiency values during the
verification period than during the calibration period.
3. Hydrologic modeling
To evaluate the hydrologic significance of the meteorological assumptions, we applied the Distributed
Hydrology Soil Vegetation Model with 14 sets of met
input (Table 4). Model skill in simulating hourly streamflow, and predicted major fluxes of the water balance
were compared across met inputs. Simulation using the
met input with observed hourly data (P1) was compared
to simulations using derived hourly values, either the
full set of techniques for best fit (P2), or the minimal
set of techniques (P3). Met input P3 was generated using
just Tmin , Tmax , P d , and grand mean wind speed, and
represents a typical hourly met input that would be gen-
TABLE 3. Meteorological model skill for H and W. Hourly variables except atmospheric transmittance, which is daily. See appendix for
efficiency equations.
Model
Period
Biasa
E 1b
E91 c
E01 d
Relative humidity
4a
4b
4c
4d
4e
4a
4b
4c
4d
4e
WY80–89
WY80–89
WY80–89
WY80–89
WY80–89
WY90–98
WY90–98
WY90–98
WY90–98
WY90–98
0.831
0.935
0.941
0.941
1
0.832
0.938
0.946
0.946
1.001
20.183
0.417
0.435
0.544
0.703
20.284
0.392
0.356
0.534
0.695
22.054
20.506
20.46
20.176
0.233
22.296
20.559
20.652
20.195
0.218
22.981
20.963
20.903
20.534
0
23.141
20.959
21.076
20.502
0.017
Wind speed
5a
5b
5a
5b
WY80–89
WY80–89
WY90–98
WY90–98
0.98
1
1.002
1.288
0.179
0.393
0.139
0.295
20.296
0.042
20.379
20.13
20.353
0
20.451
20.189
Ratio of simulated to observed mean.
Efficiency relative to grand mean of observations.
c
Efficiency relative to [month, hour] categorical mean, except [month] for atmospheric transmittance.
d
Efficiency relative to [month, hour, precip] categorical mean, except [month, precip] for atmospheric transmittance.
a
b
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WAICHLER AND WIGMOSTA
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FIG. 6. Mean hourly relative humidity by month, verification period (WY94–98). Simulated values using [month, hour, precip] means
from calibration period (method 4e, Table 1).
erated under typical circumstances in many watershed
applications. Met input P4 was identical to P1 except
for precipitation, which was the observed daily total
distributed uniformly over 24 h. Met input P5 was like
P1 except a relative [month, hour] distribution of daily
observed rainfall was used in place of a uniform distribution. We also compared met inputs based on
CS2MET daily data, because in a related study we needed the longer record available at CS2MET. The set of
best techniques and categorical bias corrections were
FIG. 7. Mean hourly wind speed by month, verification period (WY90–98). Simulated values are [month, hour, precip] means from
calibration (method 5b, Table 1).
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TABLE 4. Climate inputs to DHSVM.
Input*
P1. Observed
P2. Full simulated
P3. Minimum simulated
P4. Uniform precipitation
P5. Relative precipitation
C1. Full simulated
C2. Basic air temperature
C3. Dewpoint humidity
C4. Enhanced dewpoint
humidity
C5. Sine humidity
C6. Wind 5 0.65
C7. General solar
C8. Categorical solar
C9. Basic precipitation
Description
PRIMET hourly data
From PRIMET daily data, using
all available variables and
methods to get best match for
each hourly input variable
(methods 1b, 2, 3b, 4e, 5b)
From PRIMET daily data and
PRIMET wind, using only Tmin,
Tmax, P d, and wind 5 0.65 m
s21 (methods 1a, 2, 3a, 4a)
PRIMET hourly data except precip 5 PRIMET daly total/24
(method 2a)
PRIMET hourly data except precip 5 [month, hour] fraction
of PRIMET daily total (method 2b)
From CS2MET daily data, using
all available variables and
methods to get best possible
match to PRIMET data for
each hourly input variable
(methods 1b, 2, 3b, 4e, 5b)
Sine curve used, but not shift or
bias corrections (method 1a)
Based on dewpoint 5 Tmin (method 4a)
Based on enhanced dewpoint
model, Tdew 5 aTmin 1 b
(method 4b)
Sine curve used, but not shift or
bias corrections (method 4c)
Constant wind speed 5 0.65 m
s21 (grand mean)
Bristow and Campbell (1984)
model with their parameters
based on Pullman, Seattle, and
Great Falls (A 5 0.70, C 5
2.4, and B 5 0.036e20.154DT ,
where DT 5 mean monthly
temperature difference) (method 3a)
[month, hour, precip] means from
calibration period (method 3c)
No bias correction
* C2–C9 are identical to C1 except for the variable noted.
used to develop met input C1. Inputs C2–C9 are variants
of C1, where one of the variables was predicted with a
simpler technique, as described in Table 4.
a. Model application
DHSVM is a distributed and physically based hydrology model designed for mountainous watersheds
(Wigmosta et al. 1994, 2002; Storck et al. 1998).
DHSVM was calibrated on watershed WS2 using met
input P1 for the periods WY94–98 and WY80–83, and
met input for WY58–62 that was derived with the same
methods as C1. Calibration also included the adjacent
watershed WS1 during WY58–62, when it had an oldgrowth vegetation cover like WS2. Precipitation and
VOLUME 4
streamflow were the only measured water fluxes for the
watersheds, so calibration and verification were focused
on streamflow. Evapotranspiration and groundwater recharge were the other loss terms in the simulated water
balance. Calibration consisted of trial-and-error adjustment of hydraulic conductivity, soil depth, and coefficients for predicting macropore flow. Adjustments were
made to all soil types by either setting a uniform value
if no a priori data were available for different soil types,
or by scaling all soil-specific a priori values uniformly.
Hourly met values were representative of the PRIMET location at 430-m elevation. Spatial distribution
of the PRIMET point values to all grid cells in WS2
was required to run DHSVM. Air temperature and solar
radiation were the only variables involving significant
modification from the point values. Air temperature was
lapsed with a positive rate corresponding to a lower
inversion zone below 700-m elevation, and an upper
negative rate, using monthly break-point elevations and
lapse rates as described in Rosentrater (1997). Means
and standard deviations for the lower and upper lapse
rates were (2.7, 1.38C km 21 ) and (25.2, 1.18C km 21 ),
respectively. Solar radiation was distributed by taking
into account local slope and aspect (but not topographic
shading) for the direct beam component. Precipitation
in the real WS2 probably has a positive lapse rate with
elevation, but it was not lapsed in the model because
of water balance difficulties discussed in Waichler et al.
(2002; manuscript submitted to Water Resour. Res.).
Relative humidity and incoming longwave radiation
were distributed without modification, a reasonable assumption for this small watershed. Actual spatial variability in humidity and longwave radiation were probably small compared to other sources of model error.
The PRIMET wind speed was distributed without modification except to enforce a minimum of 0.01 m s 21 to
avoid dividing by zero when computing aerodynamic
resistance. In reality, mean wind speed is probably significantly more near the ridge top of WS2 than at the
valley-bottom PRIMET location. To the extent that this
was true, the hydrologic model underpredicted basin
evapotranspiration.
b. Fluxes
The derived met input for PRIMET using the set of
best techniques (P2) resulted in slightly lower efficiency
and more error in mean annual streamflow compared to
using the observed data (P1) (Fig. 8). The most important difference between the two simulations was the
air temperature input, which was slightly colder on average with the derived input P2 and caused more precipitation to fall as snow. The different outcomes of P2
and P3, where P3 had the met input derived with the
minimal set of techniques, are best understood after considering the single-variable differences in C2–C9 compared to C1, and P4 compared to P1.
Met inputs C2–C9 were identical to C1 except for
APRIL 2003
WAICHLER AND WIGMOSTA
259
FIG. 9. Flood magnitudes, from applying the log-Pearson type III
model (USGS 1982) (2 to 20 yr) to hourly streamflows simulated
with alternative meteorology inputs. Point estimate for flood flow
(middle line), denote 95% confidence interval (top and bottom lines).
FIG. 8. (a)–(f ) Comparison of hydrologic results across meteorological inputs. Period is all years, WY80–98. Total snowmelt varied
among model runs with identical temperature and precipitation inputs
because sublimation varied.
one variable. In C2, a lack of shift and bias corrections
for air temperature caused temperature to be colder on
average than C1, greatly increasing the amount of snowfall and slightly lowering evapotranspiration in C2. In
C3, the Tdew 5 Tmin assumption for generating hourly
humidity resulted in significantly higher evapotranspiration (ET) and lower streamflow. In the real system,
the dewpoint is often reached before the minimum air
temperature, and therefore the atmosphere is often saturated and ET is minimal over a portion of the day. In
C4, the enhanced dewpoint model (method 4b) resulted
in a smaller but still noticeable ET increase. In C5, a
similar result was obtained when a sine curve without
shift and bias corrections was used for humidity (method
4c). In C6, use of the grand mean to set a constant wind
speed of 0.65 m s 21 resulted in a slight decrease in ET
and increase in streamflow. In C7, the large positive
bias in atmospheric transmittance stemming from use
of the literature parameter values in the BC model
(method 3a) caused R s and ET to increase. In C8, using
the categorical means model for T r had little effect on
the hydrology. In C9, the lack of the 24.4% bias correction for precipitation resulted in a positive streamflow
error of 10% and reduced efficiency, confirming the
sensitivity of streamflow to this primary term in the
water balance.
Hydrology results from the minimal met input P3 were
much different from those of the data, met input P1. The
annual streamflow error was 220% with P3, caused by
much higher ET. The main reason for the much higher ET
in the P3 run was the Tdew 5 Tmin assumption for generating
humidity. The large positive bias in atmospheric transmittance associated with method 3a also contributed to the
large ET in P3, as did the higher temperatures with method
1a. Between P2 and C1, the two met inputs derived with
the set of best-fit techniques, C1 had higher efficiency
because the use of bias corrections in C1 caused air temperature to more closely match the data than in P2. Making
precipitation uniform over the day in P4 caused efficiency
of predicted streamflow to decrease slightly compared to
P1, and using a relative distribution for P5 gave results
that were essentially the same as P4. Evapotranspiration
was slightly increased in P4 due to greater interception of
precipitation, but much less so than in P3, with the result
that mean annual streamflow error was much lower in P4
than P3.
Differences in hydrology model skill were evaluated
for several subperiods within WY80–98 (Table 5). As
expected, skill was higher during the calibration period
than the verification period. DHSVM was calibrated using periods with a range of dry to wet years, and bias
is opposite in sign for dry and wet periods for most met
inputs. Bias was optimal during the relatively dry period
of WY90–92. Efficiency was optimal during the relatively wet period of WY95–97. Most affected during
the dry period was E19 , which is more sensitive to model
fit at low flows than E. A seasonal perspective of model
skill was obtained by computing efficiency E1 of monthly total streamflow separately for each month, with n
5 19 yr (Table 6). Highest skill was obtained for the
high-flow months December–March, and lowest skill
was obtained for the low-flow months of June–September. During the summer months the observed average
was a better predictor than the model in most cases
260
C9
0
0
1
22
3
23
213
3
1
23
220
8
C8
0
0
1
21
3
22
210
0
0
21
218
6
VOLUME 4
(negative model efficiency), indicating a weak simulation of baseflow. Simulation P1 had the fewest months
with negative efficiency (three), while P3 and C3–C5
had the most months (six). Simulations P2 and C1 each
had 4 months with negative efficiency. Average efficiency, weighted by proportion of annual flow in each
month, ranged from just 0.08 (C4) to 0.45 (C6).
c. Flooding frequency
* Periods refer to meteorology input. Calibration 5 WY80–89, verification 5 WY90–98, dry 5 WY90–92, wet 5 WY95–97.
1
21
21
21
3
23
28
0
1
21
216
7
0
0
1
21
3
22
210
21
0
0
218
5
0
0
23
1
3
23
25
0
3
23
213
4
C7
C6
C5
0
0
2
21
3
23
28
0
1
22
214
7
0
0
21
2
3
23
27
21
1
22
215
6
0
0
2
22
7
27
211
22
6
28
212
29
0
0
1
21
3
23
29
0
2
22
217
6
C4
C3
C2
C1
24
4
10
1
3
23
23
0
21
0
29
7
P5
P4
24
4
10
1
3
23
22
21
21
0
29
6
5
26
25
24
6
25
21
27
3
24
29
25
3
24
1
26
1
21
21
0
27
7
25
11
P3
P2
P1
23
3
13
0
2
21
29
3
22
1
216
9
Period*
Calibration
Verification
Dry
Wet
Calibration
Verification
Dry
Wet
Calibration
Verification
Dry
Wet
Bias
Bias
Bias
Bias
E
E
E
E
E91
E91
E91
E91
Statistic
TABLE 5. Change in streamflow modeling skill from entire period (WY80–98) to subperiods. Change is rounded to nearest percent. Bias is the ratio of mean simulated to mean observed
streamflow. E 5 efficiency; E91 5 first-degree efficiency based on [month, hour] means.
JOURNAL OF HYDROMETEOROLOGY
As a final exploration of the hydrologic consequence
of the various met assumptions, the observed and simulated streamflows were processed with the U.S. Geological Survey (USGS) statistical model for flood frequency, using a log-Pearson type III distribution for
annual maximum flows (USGS 1982). Point estimates
and 95% confidence intervals (CI) for flows corresponding to recurrence intervals 1.1, 2, 5, 10, and 20 yr were
computed. A regional skew coefficient of 0.12 was used
to compute a weighted skew coefficient. There were no
outliers, and the rest of the computations followed the
USGS methods. The CIs for all simulated streamflows
(P1–C9) were compared to the CI for the observed
streamflow, and in all cases there was overlap, indicating
no significant difference between the flood streamflows
predicted by statistical model (Fig. 9). However, the
point estimate from the observations was markedly
higher than the simulations at recurrence intervals above
2 yr. These two results indicate that the met inputs were
equally satisfactory for applying the USGS method, but
overall the simulations lost value compared to the data
as the recurrence interval and flood magnitude increased.
4. Discussion
We evaluated some simple methods for generating
subdaily meteorological values from limited daily data,
using a mountainous setting in a maritime climate as
the test case. The usefulness of the modified sine curve
method for predicting subdaily air temperature was confirmed by this study. The beneficial effect of the 22 h
phase shift for the air temperature and relative humidity
time series at this location was somewhat surprising,
however. The shaded conditions of the observation sites
can explain why evening cooling began earlier than predicted by the model, but cannot explain why morning
warming also began earlier than predicted. The bias
corrections used to complete the synthesis of PRIMET
air temperature from CS2MET daily Tmin and Tmax were
substantial and significantly affected the precipitation
phase in DHSVM. Without the mostly positive corrections, much more snowfall was predicted. The superior
fit of the categorical means model for atmospheric transmittance, as compared to the BC model with literature
parameter values, was also unexpected. This indicates
that using categorical means rather than the uncalibrated
BC model may be more productive in locations where
0.48
0.69
0.64
0.17
0.15
20.14
21.88
21.85
20.61
0.37
0.25
0.65
0.43
C9
C8
C7
0.49
0.73
0.61
0.06
0.03
20.21
21.93
21.87
20.60
0.32
0.38
0.67
0.43
0.47
0.69
0.67
0.29
0.30
20.01
21.79
21.81
20.57
0.34
0.22
0.65
0.45
C6
C5
0.45
0.70
0.58
20.07
20.06
20.33
22.02
21.93
20.63
0.35
0.33
0.64
0.38
0.45
0.71
0.62
20.02
20.04
20.30
21.96
21.92
20.60
0.39
0.32
0.65
0.40
C4
C3
0.52
0.67
0.39
20.56
20.33
20.49
22.12
22.0
20.72
0.21
0.54
0.71
0.33
0.18
0.20
0.36
21.22
0.03
0.06
21.75
21.77
20.56
0.32
0.25
0.45
0.08
C2
C1
0.43
0.68
0.62
0.15
0.18
20.12
21.88
21.85
20.59
0.36
0.25
0.63
0.41
0.32
0.60
0.53
0.10
0.22
20.06
21.79
21.73
20.45
0.46
0.30
0.67
0.38
P5
P4
0.31
0.60
0.53
0.11
0.21
20.07
21.8
21.79
20.44
0.46
0.30
0.66
0.38
0.47
0.50
0.40
20.36
20.27
20.46
22.09
21.96
20.58
0.09
0.63
0.71
0.33
P3
P2
0.26
0.47
0.45
0.23
0.04
20.35
21.97
21.91
20.54
0.29
0.24
0.65
0.32
0.28
0.62
0.50
0.27
0.39
0.15
21.57
21.45
20.38
0.08
0.26
0.72
0.41
P1
Month
0.29
0.61
0.60
0.20
0.29
20.04
21.83
21.82
20.48
0.22
0.04
0.55
0.34
WAICHLER AND WIGMOSTA
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Avg
TABLE 6. Efficiency (E1 ) of monthly streamflow, computed separately for each month across 19 water years (WY80–98). Negative E1 implies the observed mean is a better predictor than
the model. Avg is weighted average, where weights are fraction of obs annual flow in each month.
APRIL 2003
261
some solar radiation data exists. For relative humidity,
the categorical means model had the best fit of five tested
models, including two models that used daily Hmin and
Hmax .
We focused on time series at one location and have
not evaluated the problem of distributing met variables
spatially, nor have we tested the temporal disaggregation
techniques in other environments. However, we and others have used these techniques successfully in hydrologic modeling of diverse environments within the
northwest: eastern Washington, northwestern Montana,
and western British Columbia. These areas included
rain-, rain/snow-, and snow-dominated zones. If subdaily data are available for some time period, and met
model calibration or calculation of categorical means is
feasible, then one of the options presented here should
work reasonably well in most climates. Of the techniques that required no prior calibration or calculation
of categorical means (methods 1a, 2a, 3a, 4a, 5a), we
would expect that only the modified sine curve for air
temperature (method 1a) would yield satisfactory results
in a wide range of climates outside the western United
States. The assumption of uniform subdaily precipitation (method 2a) is probably fine for modeling areas
without significant convective storms—which includes
the maritime and snow-dominated portion of the western
United States, where most of the streamflow in the region is produced. Precipitation exhibits much stronger
diurnal tendencies in the central and eastern United
States, devaluing the uniform distribution assumption
in those areas. The Bristow–Campbell model has the
advantage of requiring no atmospheric transmittance
data when using the authors’ original parameters (method 3a), and has worked well within the northwest, but
may need recalibration to obtain satisfactory skill in
other parts of the country. The Tmin 5 Tdew assumption
(method 4a) is possible when no daily humidity data
are available, but that assumption is not reliable in semiarid and arid climates.
We emphasize that only streamflow data were available for checking the hydrologic simulations, and hydrologic results other than streamflow were useful mainly for comparing relative impacts of the different meteorological assumptions. DHSVM was calibrated with
met input P1, so it was anticipated that the corresponding model skill would be among the highest. The least
model skill resulted with input C2, which had air temperature generated with the basic method and no shift
or bias corrections. This highlights the sensitivity of
snowfall, and wintertime streamflow, to precipitation
phase in this rain/snow transition zone.
Streamflow modeling was moderately sensitive to
whether precipitation was distributed throughout the day
as observed (P1) or as a fixed distribution of the daily
total (P4, P5). We expected that hourly precipitation
input would have had more impact on model skill in
this steep and small watershed. There was little difference in simulated streamflow between using a uniform
262
JOURNAL OF HYDROMETEOROLOGY
(P4) or relative (P5) distribution, because there was little
diurnal variation in the relative distributions.
VOLUME 4
APPENDIX
Efficiency Statistics for Model Skill
5. Conclusions
Some standard techniques for disaggregating daily
meteorological data worked better than others, and in
all cases the optimal prediction capability was obtained
when some local knowledge was used. Through selection of particular methods and calibration with local
data, it was possible to generate low-bias, high-efficiency meteorological results at the study location for
all variables except wind speed. The modified sine curve
method for air temperature worked significantly better
than a [month, hour, precip] categorical mean only when
a 2-h shift was applied. A uniform or relative distribution of precipitation over the day was a better predictor than a [month, hour] categorical mean. For atmospheric transmittance, the Bristow–Campbell model
calibrated to local conditions performed best, but the
[month, precip] categorical mean was better than the
Bristow–Campbell model with regional coefficients. For
relative humidity, the [month, hour, precip] categorical
mean was the best predictor, even compared to methods
that used daily Hmin and Hmax data. The least effective
humidity model used the Tmin 5 Tdew assumption and
diurnal T variation, and should be avoided if possible.
Wind speed was the most difficult variable to reproduce,
though the [month, hour, precip] categorical mean may
have been a reasonably good predictor had confounding
measurement factors not been present.
The nature of the meteorological input was found to
significantly impact the predicted water balance and efficiency of streamflow simulation. For other uses of the
model output, such as predicting flood magnitudes with
further statistical modeling, the distinction between
model runs may be much less than the gap between
reality and simulation. The most significant differences
in streamflow efficiency were related to differences in
precipitation phase and therefore the air temperature
method used. Streamflow efficiency was more sensitive
to snow versus rain than the type of hourly distribution
of precipitation. The most significant differences in
overall water balance were related to increased evapotranspiration when the Tmin 5 Tdew humidity model was
used.
Acknowledgments. Financial support was provided by
the National Council for Air and Stream Improvement
(NCASI) and Pacific Northwest National Laboratory
(PNNL). We thank Don Henshaw for his assistance in
obtaining climate and streamflow data. Helpful comments were provided by Beverley Wemple, David
Greenland, and two anonymous reviewers. Datasets
were provided by the Forest Science Data Bank, a partnership between the Department of Forest Science,
Oregon State University, and the U.S. Forest Service
Pacific Northwest Research Station, Corvallis, Oregon.
Bias was defined as P /O , where P is the mean of
predicted (simulated) values and O is the mean of observed values. The grand mean, or mean of all values,
was used.
Four measures of efficiency are defined, in order of
increasing stringency. See Legates and McCabe (1999)
for further discussion on these statistics.
Efficiency E (Nash and Sutcliffe 1970) has been commonly used to evaluate fit of modeled quantities:
O (O 2 P ) ,
O (O 2 O)
2
E 5 1.0 2
i
i
2
(A1)
i
where
O i 5 observed value at time step i
Pi 5 predicted value at time step i.
Three first-degree efficiency measures use absolute values of differences instead of squares, reducing the influence of the largest quantities on the overall goodness
of fit. The first-degree efficiency E1 is
E1 5 1.0 2
O |O 2 P | .
O |O 2 O|
i
i
(A2)
i
The measure E1 is an improvement over E when evaluating model skill at low and moderate levels, the grand
mean but is still the basis of comparison. A further
discrimination can be made by using a categorical mean
that captures seasonal or other variation inherent in the
data: for example, a separate mean for each month
[month] or each month and hour combination [month,
hour]. The value E91 refers to first-degree, category-adjusted efficiency where the categorical mean O9 is used
instead of O in Eq. (A2). Similarly, E01 uses an additional
categorical variable to define the mean, for example,
[month, hour, daily precip status]. Avoidance of squaring and use of categorical mean instead of the grand
mean provides tougher, more revealing tests of model
skill. All of the above measures of efficiency have a
possible range of 2` to 1.0. When efficiency 5 0, the
model is no better or worse than the observed mean as
a predictor.
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