# Understanding Land–Atmosphere–Climate Coupling from the Canadian Prairie Dataset

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Prairie Station Locations

#### 2.2. Diurnal Range Definition

_{x}, and the minimum temperature, T

_{n}:

_{x}− T

_{n}

_{x}, and the minimum, RH

_{n}:

_{x}− RH

_{n}

_{m}, RH

_{m}, and recorded T

_{x}, T

_{n}, and DTR. The difference in relative humidity (RH), DRH, between T

_{n}and T

_{x}was used as an approximation of the diurnal range. However, there has been considerable discussion in recent years about the difference between DTR, T

_{x}, and T

_{n}derived from the monthly means of hourly data, and the conventional monthly mean of daily values of DTR, T

_{x}, and T

_{n}[12,17,18,19].

_{n}is near sunrise and T

_{x}is in the mid-afternoon, but advection can shift the daily minimum temperature away from the time of sunrise to a lower value than the temperature at sunrise, and similarly, advection can shift the daily maximum temperature away from the mid-afternoon to a higher value than the mid-afternoon temperature. Either will give a larger diurnal range.

_{E}), and the saturation pressure (p*) at the lifting condensation level (LCL). We defined the pressure height to the LCL, P

_{LCL}= PS − p* [2], which in the warm season, is often an indicator of the height of cloud base [9]. We calculated the diurnal ranges that are related to moist convective processes:

_{E}= θ

_{Ex}− θ

_{En}

_{LCL}= P

_{LCLx}− P

_{LCLn}

#### 2.3. Opaque Cloud Bins

_{m}. The second, OPAQSW, is a mean of the hourly opaque cloud values during daylight hours, weighted by a fit to the downward clear sky flux derived from the reanalysis known as ERA-Interim (details in [13]).

#### 2.4. Cloud Radiative Forcing

_{dn}, based on a fit to the clear-sky fluxes from the nearest grid-point of the reanalysis ERA-Interim [13,20]:

_{dn}/SWCS

_{dn}

_{dn}− SW

_{dn}= −ECA * SWCS

_{dn}

_{dn}has a large increase from the winter to the summer solstice.

_{dn}, also from ERA-Interim, as:

_{dn}− LWCS

_{dn}

_{dn}is the smaller term, and LW

_{dn}increases with increasing cloud cover, so that LWCF is positive.

_{net}= (1 − α

_{s}) SWCF + LWCF

_{s}= SW

_{dn}/SW

_{up}

_{n}= LW

_{dn}− LW

_{up}

_{dn}, and estimating LW

_{up}from the daily mean air temperature, T

_{m}(°C), from:

_{up}= ε σ T

_{k}

^{4}

_{k}(K) = T

_{m}+ 273.15, σ = 5.67 × 10

^{−8}(W m

^{−2}K

^{−4}) and the emissivity ε set to 1.

#### 2.5. Data

## 3. Climate Coupling to Opaque Cloud and Snow Cover

#### 3.1. Forcing of Diurnal Cycle by Cloud and Snow Cover

_{m}> 0 °C and no snow cover (141,160 days), and the cold group of days with T

_{m}< 0°C with surface snow cover (74,260 days). Here, we exclude the much smaller mixed group of days, above freezing with snow cover and below freezing without snow (see [14]).

_{m}. In the warm season from May to October, we see a steep increase of maximum temperature T

_{x}and diurnal temperature range DTR with decreasing opaque cloud, and a rather small fall of minimum temperature in summer. The changing day-length is clearly visible by September and October. In sharp contrast, in the cold season with snow, from December to February, T

_{x}decreases with decreasing opaque cloud, and T

_{n}decreases even more steeply to its lowest minimum at sunrise under clear skies. Beside the September and December plots, we show OPAQ

_{m}legends in ascending and descending order to illustrate this reversal of the diurnal cycle coupling to opaque cloud between warm and cold seasons.

_{m}, by about 10 °C; and second, it reverses the sign of the coupling to opaque cloud cover. Snow cover acts as a climate switch between non-overlapping regimes [11,14]. We will explore the climate impact of snow cover further in Section 3.4, but first we will show the seasonal impact on the cloud radiative forcing.

#### 3.2. Change of Cloud Forcing between Warn and Cold Season

_{dn}and LW

_{dn}, at Bratt’s Lake, which we first averaged from 1-min data to hourly means, and then to daily means.

_{net}from Equation (6b) reverses the sign from increasing negative with cloud cover in the warm season, to increasing positive in the cold season with cloud cover. This is consistent with the daily mean temperature response seen in Figure 2 to the changing opaque cloud cover.

#### 3.3. Relationship between Opaque Cloud and Cloud Radiative Forcing

_{m}> 0 °C and the cold season as days with T

_{m}< 0 °C, because we have no snow cover data for Bratt’s Lake. For the SW comparison, we compared the daytime weighted opaque cloud, OPAQSW (see Section 2.3) with ECA from Equation (3). For the LW comparison, we compared the 24 h mean OPAQ

_{m}with LW

_{n}computed from Equation (8).

^{2}= 0.87):

^{2}

^{2}= 0.71):

^{2}

_{n}on opaque cloud for days above freezing (3245 days) for three bins of daily mean RH

_{m}(<60, 60–75, >75%). The outgoing LW

_{n}flux for the same cloud cover increases as RH falls. The temperature dependence is very small when T

_{m}> 0°C (not shown). The right panel shows the dependence of LW

_{n}on opaque cloud for temperatures below freezing (2198 days) for three bins of daily mean T

_{m}(<−20, −20 to −10, −10 to 0 °C). The outgoing LW

_{n}flux now decreases with colder temperatures, probably because the surface cools under a stable BL in the cold season [13].

_{n}on quadratic opaque cloud and RH

_{m}gives (R

^{2}= 0.91):

_{n}= −128.6(±7.8) + 28.1(±1.8)OPAQ

_{m}+ 44.6(±1.8)OPAQ

_{m}

^{2}+ 0.49(±0.01)RH

_{m}

_{m}and RH

_{m}gives (R

^{2}= 0.83):

_{n}= −112.2(±9.8) + 43.5(±2.8)OPAQ

_{m}+ 26.8(±2.5)OPAQ

_{m}

^{2}+

0.29(±0.02)RH

_{m}− 1.02(±0.03)T

_{m}

#### 3.4. Climate Impact of Snow Cover

_{m}, with snow cover, derived from Figure 2 by calculating the difference of the diurnal composites with and without snow for the transition months, November and March, for each opaque cloud cover bin. We made a correction of about 2 °C, based on the mean seasonal cycle [14], to allow for the fact that the mean date of the snow-free composite is about 15 days earlier in November, and later in March than the composite with snow. The curves are a little noisy, because the independent sampling in opaque cloud bins, with and without snow, is far from homogeneous, and in these transition months, the number of days in each bin ranges widely from 184 to 1869 (not shown). Nonetheless, we see a larger degree of cooling as the opaque cloud decreases. The climate cooling with snow, averaged across all cloud bins (open circles), is −11.8 °C (−10.7 °C) for November (March). We also show quadratic fits (dashed) as a useful smooth reference for the impact of cloud cover. We note that the radiative forcing is stronger in March than November, but we cannot assess whether the small difference between the November and March curves is significant, given the inhomogeneity across the cloud bins.

_{M}, for October to April against the fraction of days with snow cover (FDS) for five stations in Alberta, Lethbridge, Medicine Hat, Calgary, Red Deer, and Grande Prairie, listed in order of increasing latitude (adapted from [11,15]). The line fit shown is for 326 years of data, and we show the station means (black circles) that lie close to this line fit. Since it is clear that the southern three stations (red points) have warmer temperatures and lower FDS than the northern two stations, we also computed the linear regression slopes for these two groups.

_{M}= 3.9(±1.2) − 14.6(±0.5) * FDS (R

^{2}= 0.79)

_{M}= 3.8(±1.5) − 14.3(±0.7) * FDS (R

^{2}= 0.73)

_{M}= 3.2(±1.5) − 13.6(±1.5) * FDS (R

^{2}= 0.48)

#### 3.5. Coupling of Warm Season Diurnal Ranges and 24-h Imbalances to Opaque Cloud

_{E}, and DP

_{LCL}from similar diurnal composites (not shown). Close examination of Figure 2 shows that there is a discontinuity across local midnight that changes with opaque cloud cover. So we calculated, also for the first time, this 24 h imbalance of the diurnal cycle as a function of opaque cloud and month. These are key conceptual improvements in our understanding of the diurnal cycle over land in the warm season, and our results are robust as there are about 20,000 days per month.

_{m}are:

_{m}− 6.0(±0.7) * OPAQ

_{m}

^{2}(R

^{2}= 0.992)

_{m}− 38.9(±1.4) * OPAQ

_{m}

^{2}(R

^{2}= 0.996)

_{m}= 1, given by these fits, are the small values (DTR, DRH) = (1.4 °C, 6.0%).

_{m}< 0.4, and the increase of precipitation with OPAQ

_{m}is largest in summer, peaking in July when T and the mixing ratio Q also peak. However, because June has substantially greater opaque cloud cover [12], mean June precipitation (2.28 mm d

^{−1}) is greater than July (1.91 mm d

^{−1}).

_{24}and ΔRH

_{24}, which we calculated from the discontinuities across local midnight [14]. We see that over the range of OPAQ

_{m}from 0.05 to 0.95 (nearly clear to nearly opaque cloud cover), the mean (ΔT

_{24}, ΔRH

_{24}) change monotonically from (+2 °C, −6%) to (−1.5 °C, +6%). Under nearly clear skies, the warming, and drying over the diurnal cycle is slightly larger in April, May, and June when the mean temperature is increasing seasonally, and slightly smaller in August and September. Under cloudy skies, there is a larger increase in ΔRH

_{24}in April and May. The SE of the hourly binned data from which Figure 6 is derived as ≈0.1 K for T, ≤0.5% for RH.

_{24}, and ΔRH

_{24}cross zero for OPAQ

_{m}= 0.45. This presents a conceptual challenge for equilibrium models for the non-precipitating convective BL over land [21].

_{E}and P

_{LCL}. The spread in the diurnal ranges and the diurnal imbalances is again small from April to September. For the 6-month means, the quadratic regression fits for the OPAQ

_{m}dependence are:

_{E}= 19.7(±0.7) − 9.4(±1.2) * OPAQ

_{m}− 7.5(±1.2) * OPAQ

_{m}

^{2}(R

^{2}= 0.983)

_{LCL}= 181.4(±4.9) − 90.3(±9.0) * OPAQ

_{m}− 81.1(±8.7) * OPAQ

_{m}

^{2}(R

^{2}= 0.991)

_{E}, P

_{LCL}) = (19.7 K, 181.4 hPa) from the morning sunrise minimums. The cloudy limit for OPAQ

_{m}= 1, given by these fits, are the small values (Dθ

_{E}, DP

_{LCL}) = (2.73 K, 10.0 hPa).

_{E24}and +18.6 hPa for ΔP

_{LCL24}, which are 14.9% and 10.5% of the respective diurnal ranges. There is a corresponding small 24 h imbalance of mixing ratio, ΔQ

_{24}, of +0.2 g kg

^{−1}(not shown). At the other limit under nearly-overcast skies, typically with rain, the 24 h imbalance is a fall of −2.6 K for Δθ

_{E24}and −14.6 hPa for ΔP

_{LCL24}, with a corresponding fall of ΔQ

_{24}of −0.24 g kg

^{−1}(not shown). The SE of the hourly binned data from which these plots are derived is ≤0.3 K for θ

_{E}and ≤1.5 hPa for P

_{LCL}. On the seasonal timescale, we see that the imbalance of Δθ

_{E24}is larger in April, May, and June over most of the OPAQ

_{m}range as the climate warms, and smaller in August and September. However for ΔP

_{LCL24}, the seasonal response has an asymmetric structure that is consistent with ΔRH

_{24}, since a lower RH is tightly coupled to a higher P

_{LCL}.

_{E}and P

_{LCL}. At the cloudy extreme with rain, we see 24 h imbalances of opposite sign that are generally slightly smaller. These rather precise warm-season patterns across opaque cloud cover, and therefore cloud radiative forcing, set a clear target for modeling the partially cloudy boundary layer over land.

## 4. Hydrometeorological Memory on Monthly Timescales

_{E}, and P

_{LCL}, and the diurnal ranges defined in Equations (1) and (2).

_{m}, the maximum and minimum, Y

_{x}and Y

_{n}, and the times of the maximum and minimum [16]. We then computed the long-term station monthly mean, and used these to compute monthly anomalies, δY. For the daily precipitation and snow-depth, we also computed monthly means, the long-term station monthly means, and used these to compute monthly anomalies for each station. The monthly anomalies of opaque cloud, precipitation, snow depth, and snow cover frequency were then standardized by their monthly standard deviation (SD). For the temperature anomalies, δT

_{m}, δT

_{x}, δT

_{n}, and the diurnal temperature range, δDTR, we standardized by the monthly SD of δT

_{m}. Similarly for the variables, δRH

_{m}, δRH

_{x}, δRH

_{n}and the diurnal RH range δDRH, we standardized by the monthly SD of δRH

_{m}. The corresponding set of anomalies for equivalent potential temperature, δθ

_{E}, and pressure–height to the LCL, δP

_{LCL}, were standardized by the monthly SD of δθ

_{Em}, and δP

_{LCLm}respectively.

_{m}) for the current month, and lagged precipitation anomalies for the current month (δPR0) and preceding months (δPR1, δPR2, δPR3, δPR4, δPR5) in the form:

#### 4.1. Memory of Cold Season Precipitation in April Climatology

_{m}by 10 °C (Figure 2 and Figure 5). April is the month when the snowpack finally melts and the ground thaws. The upper group in Table 2 shows selected April standardized anomalies regressed on standardized anomalies of opaque cloud for April; and precipitation from April back to November (coefficients A to G in Equation (15)). We see that the April monthly anomalies show memories of the anomalies of precipitation 5 months back through the entire cold season to November, when typically the ground begins to freeze, and the first lasting snow occurs (Figure 5). Some of this memory remains in the March snowpack depth (not shown here, see [16]).

_{x}, and δP

_{LCLx}, mean that these variables decrease with increasing opaque cloud cover, while the positive sign for the δRH

_{n}and δRH

_{m}means that they increase with opaque cloud. For δT

_{x}and δDTR (and δT

_{m}, not shown), the negative coefficients B to G, for the months March back to November, mean that the positive cold season precipitation anomalies are correlated with cold April temperatures. For δRH

_{n}, δRH

_{m}(and δRH

_{x}, not shown), the positive coefficients, B to G, mean that positive cold season precipitation anomalies are correlated with higher RH in April. Most coefficients for δDTR, δRH

_{n}, δRH

_{m}, and δP

_{LCLx}(representative of afternoon cloud-base) have a 99% confidence (p < 0.01).

_{m}-Apr + B * δPR-Apr + C * δPR-Mar + D * δPR-Feb +

E * δPR-Jan + F * δPR-Dec + G * δPR-Nov + S * δSnowCover-Apr

^{2}for all variables, and especially for T

_{x}, with the addition of snow cover. For maximum temperature, T

_{x}, snow cover frequency anomalies have as large an impact as opaque cloud anomalies. Note that the coefficients G for δPR-Nov for δRH

_{n}, δRH

_{m}, and δP

_{LCLx}are not significant, but the coefficients G for δDTR and δT

_{x}have a confidence >99% in Table 2. It is possible that this is the cooling impact in April coming from the melt of soil–ice that was frozen back in November.

#### 4.2. Growing Season Memory of Precipitation

_{n}, δRH

_{m}, δP

_{LCLx}with high R

^{2}values, are correlated with precipitation anomalies going back three months. As in Table 2, the OPAQ coefficients A are typically the largest, except notably for δQ

_{m}.

_{x}, δT

_{m}, δT

_{n}, and δDTR, which were all standardized by the SD of δT

_{m}. The fit represented by R

^{2}is largest for DTR, and it decreases from δT

_{x}to δT

_{n}. All the temperature variable anomalies show a strong inverse correlation with opaque cloud anomalies that reflect the downward SW radiation. The warm season is dominated by negative SWCF as shown in Figure 3. The negative values of A decrease from δT

_{x}to δT

_{n}. δDTR has a negative correlation to both cloud anomalies, and to the precipitation anomalies going back three months. Note that because all the temperatures were standardized by the SD of δT

_{m}, the coefficients for the diurnal range are the difference of the corresponding coefficients for the maximum and minimum. For example, A(δDTR) = −0.61 = A(δT

_{x}) − A(δT

_{n}), and B(δDTR) = −0.26 = B(δT

_{x}) − B(δT

_{n}) (rounded to two significant figures). We see that the coefficients B change sign in the sequence from δT

_{x}to δT

_{m}to δT

_{n}. We also see that T

_{m}falls strongly with cloud, but its coupling to precipitation is weak because the coefficients B and C have opposite signs. This regression analysis clearly shows that mean temperature anomalies, δT

_{m}, are strongly coupled to cloud, and therefore solar forcing, but rather weakly to precipitation, while δDTR (and δT

_{x}) decrease with both cloud and precipitation. We cannot infer causality from multiple regressions, but negative B for δT

_{x}is consistent with evaporation from moist soils reducing T

_{x}, and the positive B for δT

_{n}is consistent with the fact that under wetter conditions, the fall of T

_{n}at night is limited by saturation.

_{x}, δRH

_{m}, δRH

_{n}, and δDRH. For the first three, the regression coefficients show that positive RH anomalies are correlated with positive cloud and precipitation anomalies, and the coefficients are significant for both the present and three past months. The coefficients for δDRH are negative because δRH

_{n}increases faster with cloud and precipitation than δRH

_{x}, and the coefficients are significant for only one past month. The R

^{2}fit decreases monotonically from the afternoon minimum δRH

_{n}to δRH

_{m}to the sunrise maximum δRH

_{x}to δDRH. The diurnal cycle of T and RH have an inverse dependence on opaque cloud, reaching T

_{x}and RH

_{n}in the afternoon at the same time [16]. This is related to the fact that mixing ratio Q is tightly constrained by BL transports, which we will discuss in Section 4.3. However, over land, near-surface RH is constrained by the availability of soil moisture for evaporation from bare soil and transpiration (which is often modeled as a stomatal resistance to evaporation [22,23]. Soil moisture anomalies are related in turn to precipitation anomalies. We see that afternoon RH

_{n}and mean RH

_{m}anomalies have a strong positive correlation to precipitation anomalies, and a large R

^{2}. However, RH

_{x}, which increases with precipitation, is limited if the surface saturation is reached and dew forms before sunrise. Because the latent heat release slows the temperature fall, it is consistent that RH

_{x}and T

_{n}anomalies are both positively coupled to wetter precipitation anomalies for the current month (coefficient B).

_{LCL}anomalies: P

_{LCLx}is generally representative of afternoon cloud-base [9]. P

_{LCL}has a strong dependence on RH and a weak dependence on T, and we see that negative P

_{LCL}anomalies are coupled to positive cloud and precipitation anomalies. The coefficients are largest for afternoon δP

_{LCLx}, for which R

^{2}is high. The coefficients for δP

_{LCLx}, δP

_{LCLm}, and δP

_{LCLn}are all 99% significant for both the present and three past months, showing that cloud-based anomalies have a long memory of precipitation anomalies in the growing season.

_{Ex}, δθ

_{Em}, δθ

_{En}, and δDθ

_{E}. The first three show the decrease with increased cloud, but an increase with precipitation. The R

^{2}values are small, even though the coefficients have 99% confidence. The diurnal range of θ

_{E}is dominated by the dependence of DTR on opaque cloud. The two afternoon anomalies, δθ

_{Ex}and δP

_{LCLx}, are related to moist convective instability, which is favored by a higher θ

_{Ex}and a lower cloud base.

_{m}. The R

^{2}fit is much smaller for Q than for RH. The negative correlation to opaque cloud is small, because T and RH have an inverse diurnal dependence on cloud. The positive correlation to precipitation anomalies goes back two months, consistent with positive precipitation anomalies increasing evapotranspiration.

_{x}, δRH

_{n}, δP

_{LCLx}are strongly correlated to opaque cloud anomalies. Correlation with precipitation anomalies are weaker, but stretch back for three past months for these key variables. Anomalies of Q

_{m}are coupled to precipitation anomalies with memory of two months past, but they have weak correlations to opaque cloud.

#### 4.3. Growing Season Coupling of the Diurnal Cycle to Precipitation and Cloud

^{2}, such as DTR, RH

_{n}, and P

_{LCLx}, because these have the ratio of the coefficients B/C ≈ 1.5 in Table 3.

_{m}= δOPAQ

_{m}+ 0.46, where 0.46 is the mean opaque cloud over all the months. For each MJJA month (total 2466 months), we computed the weighted anomaly δPRwt from (17), and added the MJJA mean precipitation rate of 1.8 mm d

^{−1}to give PRwt = δPRwt + 1.8. We then stratified the data into three ranges of PRwt of <1.2 mm d

^{−1}; 1.2 to 2 mm d

^{−1}, and >2 mm d

^{−1}, which have mean values of 0.9, 1.6, and 2.6 mm d

^{−1}. There are (531, 1103, 832) months in these three PRwt bins. To generate Figure 7, we compute for each variable bin, the mean and standard error (SE) of the anomalies, and add back the MJJA variable means.

_{x}and T

_{n}, the top-right shows DRH, RH

_{x}and RH

_{n}, the bottom-left shows Dθ

_{E}, θ

_{Ex}, and θ

_{En}and the bottom-right is DP

_{LCL}, P

_{LCLx}, and P

_{LCLn}. The strong dependence on opaque cloud, seen in Figure 6, clearly dominates most of these climate variables, since T falls and RH increases with increasing cloud. This is turn is connected to the weak dependence of Q on cloud (Table 3). The color scheme is red and blue, respectively, for the dry and wet precipitation bins. As PRwt falls, DTR increases faster than T

_{x}.

_{x}and RH

_{n}(and RH

_{m}, not shown) increase with both cloud and PRwt, but because afternoon RH

_{n}increases faster than RH

_{x}, DRH decreases with increasing PRwt. Note the rise of RH

_{x}with PRwt towards saturation. If RH

_{x}reaches saturation at the surface on individual days, condensation of dew and the release of latent heat limit the fall of T

_{n}.

_{LCLx}and θ

_{Ex}determine the cloud-base height and moist adiabat. Both θ

_{Ex}and θ

_{En}increase with PRwt, but the diurnal range Dθ

_{E}depends primarily on cloud instead of precipitation, as shown in Table 3. All of the P

_{LCL}variables decrease with increasing PRwt. The sunrise minimum of P

_{LCLn}falls with PRwt, as the surface moves towards saturation. Thus, higher precipitation, which we can loosely associate with increased daytime evapotranspiration (ET), corresponds with a lower monthly mean cloud base and a higher θ

_{E}in the afternoon, which would both favor increased convective instability.

_{m}, and weighted precipitation anomalies, δPRwt, from Equation (17) in mm d

^{−1}, from the MJJA growing season merge of 2466 months.

_{m}into four ranges: δOPAQ

_{m}< −0.08; −0.08 to 0; 0 to 0.08, and >0.08, based on the SD of δOPAQ

_{m}≈ 0.08. There are (371, 839, 909, 347) months in these respective bins. We averaged in bins the diurnal cycle of the anomalies from the station monthly means, calculate the SE, and added back the 12-station MJJA mean of Q. The legend shows the mean value for each δOPAQ

_{m}bin, and in parentheses the corresponding mean of δPRwt. As the mean δOPAQ

_{m}increases from −0.12 to +0.12, the mean δPRwt increases from −0.43 to +0.42 mm d

^{−1}. We have binned by δOPAQ

_{m}, but mean OPAQm and precipitation increase together (Figure 6). The small increase in Q

_{m}with δOPAQ

_{m}is consistent with Table 3.

^{−1}, based on the SD of δPRwt ≈ 0.7 mm d

^{−1}. There are (387, 961, 745, 373) months in these respective bins. The legend shows the mean value for each δPRwt bin, and again in parentheses the corresponding mean of δOPAQ

_{m}. With increasing δPRwt, there is a large upward shift of the mean diurnal cycle of Q, as Q

_{m}increases with precipitation anomalies, which we can associate with increased soil moisture and ET. As the mean δPRwt increases from −0.99 to +1.23 mm d

^{−1}, mean δOPAQ

_{m}increases from −0.05 to +0.05, and the fall of Q from mid-morning maximum to afternoon minimum is reduced as in the left panel.

## 5. Seasonal Climate Issues

#### 5.1. Seasonal Extraction of Surface Total Water Storage

^{2}= 0.56, is:

^{−1}, while the mean drawdown of TWS is 0.59 mm d

^{−1}for δPrecip(MJJA) = 0; or 25% of the mean precipitation. Thus Equation (18) shows that, as δPrecip(MJJA) decreases from +1 to −1 mm d

^{−1}, ΔTWS:MJJA increases from near zero to −1.15 mm d

^{−1}, which corresponds to −141 mm over the 123 day growing season. The coupling coefficient of 0.56(±0.09) in Equation (18) is effectively a 56 ± 9% damping coefficient for precipitation anomalies in the growing season by changes in the drawdown of TWS. This drawdown of stored water in the growing season means that ET > precipitation, and this difference increases in dry summers.

#### 5.2. Impact of Land-Use Change on Growing Season Climate

_{m}and mixing ratio Q

_{tx}at the time of the afternoon T

_{x}. We averaged the 10-day means from Saskatoon, Regina, and Estevan, the three southern stations in Saskatchewan with complete datasets [10]. We show the standard errors (SE) of the difference between the two mean time series as an indication of significance. For precipitation, which has much more variability than temperature and humidity, we used monthly precipitation for the 21 stations in Saskatchewan south of 53.22° N, from the second generation-adjusted precipitation dataset [26]. Error bars are the SE of each monthly mean. The right panel shows the corresponding changes in the annual cycle of T

_{x}, P

_{LCLtx}, and θ

_{Etx}between the two time periods.

_{x}of −0.93 ± 0.09 K, and significantly moister with a rise of (RH

_{m}, Q

_{tx}) of (6.9 ± 0.2%, 0.70 ± 0.04 gkg

^{−1}). There is a corresponding fall of the P

_{LCLx}of 22.3 ± 1.1 hPa, and a small rise of θ

_{Etx}of 1.1 ± 0.2 K, both at the time of afternoon T

_{x}. There is also an increase of summer (June, July, and August) precipitation of 25.9 ± 4.6 mm.

_{LCLx}and higher θ

_{Etx}. Not shown here is a distribution shift in cloud frequency: with 6% fewer days with 2–4 tenths, and 7% more with 7–10 tenths cloud cover [10].

#### 5.3. Warm Season Atmospheric and Surface Energy Budgets

_{n}= 212 W m

^{−2}is about half the TOA downward flux. On the right is the LW budget terms, where the upward surface LW emission of 400 W m

^{−2}is mostly absorbed by the atmospheric greenhouse gases, primarily water vapor and CO

_{2}, as well as by clouds. About 10% escapes to space through the atmospheric infrared window. Clouds and atmosphere re-emit to space, and back to the surface, giving a surface LW

_{n}= −73 Wm

^{−2}. The resulting surface R

_{n}= 139 W m

^{−2}balances the upward sensible and latent heat fluxes (40 and 82 W m

^{−2}respectively), and the growing season warming of the ground of 17 W m

^{−2}, which is probably too large [31]. For the MJJA surface water budget, precipitation is 2 mm d

^{−1}and ET is 2.8 mm d

^{−1}. ET exceeds precipitation in the growing season, because of the substantial drawdown of surface water storage, as discussed in Section 5.1. The TOA SW

_{n}> outgoing LW for the MJJA warm season.

_{n}, surface SW

_{dn}, net radiation, R

_{n}, the sensible heat flux, SH, Bowen ratio, BR, and the 2 m temperatures all decrease, while the latent heat flux, LH, and precipitation increase. There is compensation between the surface SW

_{n}and LW

_{n}fluxes as reflective cloud changes, which reduces the change in R

_{n}. If there is less reflection by clouds, SW

_{dn}increases, and this warms the surface, and LW

_{up}increases. Because the decrease of cloud cover and precipitation are coupled, and ET changes much less than precipitation, we see that the surface BR increases by a factor of two as cloud cover and precipitation decrease.

^{−1}, which is largely consistent with the budget analysis in Section 5.1, based on the GRACE data. There is a substantial MJJA drawdown of about 80 mm of soil water (not shown), because the model has four soil layers to a total depth of 2.89 m with a dynamic range of water storage of 150 mm per meter between field capacity and permanent wilting point. However, the model soil water budget has additional increments, because the soil moisture reanalysis uses observed 2 m values of temperature and humidity and satellite estimates of soil moisture [32] to minimize the model 2 m temperature forecast errors. Despite this analysis correction, we found in [31] that on daily timescales, ERA-Interim in the warm season has a cold bias in T

_{x}and a warm bias in T

_{n}, so that DTR is biased low; and these biases increase under clear skies. Table 4 stratifies four-month composites by ECA, so that it is not directly comparable to the daily analysis in [31], but it is likely that T

_{x}and T

_{n}in Table 4 have respectively cold and warm biases of about 1 °C.

## 6. Conclusions

_{E}and LCL under clear skies, and a fall of both under cloudy skies.

_{LCL}, but not θ

_{E}, increase. With increased precipitation, afternoon T

_{x}falls a little, while RH

_{n}and θ

_{Ex}increase and P

_{LCLx}, representing cloud-base, falls.

^{−1}, the seasonal extraction of ground water increases from near-zero with high precipitation, to 1.15 mm d

^{−1}for low precipitation.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Climate station locations, Canadian ecozones, regional zones, agricultural regions, and boreal forest (adapted from [14]).

**Figure 2.**Monthly diurnal cycles for cold-snow and warm-no-snow classes, stratified by opaque cloud (adapted from [14]).

**Figure 3.**Mean annual cycle of CF

_{net}, stratified by effective cloud albedo (ECA) (adapted from [13]).

**Figure 4.**Relationship between opaque cloud at Regina and Bratt’s Lake ECA (

**left**), opaque cloud, and LW

_{n}stratified by RH

_{m}in the warm season (

**middle**), and (

**right**) LW

_{n}stratified by T

_{m}in the cold season (adapted from [13]).

**Figure 5.**Drop of temperature with fresh snowfall (

**top-left**), climate cooling with snow cover in November and March as a function of opaque cloud (

**top-right**), 10 °C separation of cold season climates with and without snow cover (

**bottom-left**), and (

**bottom-right**) dependence of mean cold season temperature on fraction of days with snow cover (adapted from [11,14,15].

**Figure 6.**The opaque cloud dependence of the diurnal ranges of T, RH, θ

_{E}, and P

_{LCL}(

**left**) and (

**right**) the 24 h imbalance of the diurnal cycle (adapted from [14]).

**Figure 7.**Coupling between DTR, T

_{x}and T

_{n}(

**top-left**), (

**top-right**) difference in relative humidity (DRH), RH

_{x}and RH

_{n}, (

**bottom-left**) Dθ

_{E}, θ

_{Ex}and θ

_{En}and (

**bottom-right**) DP

_{LCL}, P

_{LCLx}and P

_{LCLn}and opaque cloud fraction and weighted precipitation in mm d

^{−1}(adapted from [16]).

**Figure 8.**Dependence of diurnal cycle of the mixing ratio (Q) on opaque cloud bins (

**left**) and weighted precipitation bins (

**right**) [16].

**Figure 9.**The mean annual cycle of Gravity Recovery and Climate Experiment (GRACE) total water storage (TWS) anomaly by province (from [12]).

**Figure 10.**Long term trends in total cropland, pasture, and summer fallow around five climate stations in Saskatchewan (

**left**); (

**center**) RH

_{m}, Q

_{tx}and mean precipitation in southern Saskatchewan, and (

**right**) mean changes in annual cycle of T

_{x}, P

_{LCLtx}, and θ

_{Etx}for Saskatoon, Regina, and Estevan (adapted from [10,15]).

**Figure 11.**Schematic for surface and top-of-atmosphere (TOA) energy budgets for Prairie region of southern Saskatchewan.

Station Name (Code) | Station ID | Province | Latitude | Longitude | Elevation (m) |
---|---|---|---|---|---|

Red Deer (RD) | 3025480 | Alberta | 52.18 | −113.62 | 905 |

Calgary (CA) | 3031093 | Alberta | 51.11 | −114.02 | 1084 |

Edmonton (ED) | 3012202 | Alberta | 53.57 | −113.52 | 671 |

Lethbridge (LE) | 3033880 | Alberta | 49.63 | −112.80 | 929 |

Medicine Hat (MH) | 3034480 | Alberta | 50.02 | −110.72 | 717 |

Grande Prairie (GP) | 3072920 | Alberta | 55.18 | −118.89 | 669 |

Regina (RG) | 4016560 | Saskatchewan | 50.43 | −104.67 | 578 |

Moose Jaw (MJ) | 4015320 | Saskatchewan | 50.33 | −105.55 | 577 |

Estevan (ES) | 4012400 | Saskatchewan | 49.22 | −102.97 | 581 |

Swift Current (SW) | 4028040 | Saskatchewan | 50.3 | −107.68 | 817 |

Prince Albert (PA) | 4056240 | Saskatchewan | 53.22 | −105.67 | 428 |

Saskatoon (SK) | 4057120 | Saskatchewan | 52.17 | −106.72 | 504 |

Portage-Southport (PS) | 5012320 | Manitoba | 49.9 | −98.27 | 270 |

Winnipeg (WI) | 5023222 | Manitoba | 49.82 | −97.23 | 239 |

The Pas (TP) | 5052880 | Manitoba | 53.97 | −101.1 | 270 |

**Table 2.**Standardized regression coefficients for April anomalies in anomalies δDTR (diurnal range of temperature), δT

_{x}, δRH

_{n}, δRH

_{m}, and δP

_{LCLx}on standardized anomalies of opaque cloud and precipitation (upper group); and (lower group) adding fraction of April days with snow cover. For coefficients: plain text represents p < 0.01 (>99%); italic represents 0.01 ≤ p < 0.05, and coefficients are omitted for p > 0.05.

Variable620 months R^{2} | δDTR0.67 | δT_{x}0.47 | δRH_{n}0.65 | δRH_{m}0.63 | δP_{LCLx}0.66 |

δOPAQ_{m}-Apr (A) | −0.52 ± 0.02 | −0.78 ± 0.04 | 0.76 ± 0.03 | 0.60 ± 0.03 | −0.93 ± 0.04 |

δPR-Apr (B) | −0.06 ± 0.02 | 0.20 ± 0.03 | 0.17 ± 0.03 | −0.19 ± 0.04 | |

δPR-Mar (C) | −0.12 ± 0.02 | −0.22 ± 0.04 | 0.23 ± 0.03 | 0.19 ± 0.02 | −0.27 ± 0.03 |

δPR-Feb (D) | −0.07 ± 0.02 | −0.12 ± 0.04 | 0.16 ± 0.03 | 0.13 ± 0.02 | −0.19 ± 0.03 |

δPR-Jan (E) | −0.09 ± 0.02 | −0.19 ± 0.04 | 0.17 ± 0.03 | 0.13 ± 0.02 | −0.21 ± 0.03 |

δPR-Dec (F) | −0.06 ± 0.02 | 0.16 ± 0.03 | 0.14 ± 0.02 | −0.19 ± 0.03 | |

δPR-Nov (G) | −0.08 ± 0.02 | −0.13 ± 0.04 | 0.07 ± 0.03 | 0.08 ± 0.02 | −0.11 ± 0.03 |

Variable550 months R^{2} | δDTR0.73 | δT_{x}0.65 | δRH_{n}0.80 | δRH_{m}0.70 | δP_{LCLx}0.78 |

δOPAQ_{m}-Apr (A) | −0.49 ± 0.02 | −0.57 ± 0.04 | 0.65 ± 0.03 | 0.54 ± 0.03 | −0.82 ± 0.04 |

δPR-Apr (B) | −0.04 ± 0.02 | 0.16 ± 0.03 | 0.15 ± 0.03 | −0.15 ± 0.04 | |

δPR-Mar (C) | −0.08 ± 0.02 | −0.07 ± 0.03 | 0.14 ± 0.03 | 0.14 ± 0.03 | −0.18 ± 0.03 |

δPR-Feb (D) | −0.05 ± 0.02 | 0.09 ± 0.03 | 0.10 ± 0.03 | −0.11 ± 0.03 | |

δPR-Jan (E) | −0.05 ± 0.02 | 0.06 ± 0.03 | 0.07 ± 0.03 | −0.08 ± 0.03 | |

δPR-Dec (F) | −0.04 ± 0.02 | 0.12 ± 0.02 | 0.13 ± 0.02 | −0.16 ± 0.03 | |

δPR-Nov (G) | −0.06 ± 0.02 | −0.10 ± 0.03 | |||

δSnowCover-Apr (S) | −0.19 ± 0.02 | −0.63 ± 0.04 | 0.52 ± 0.03 | 0.31 ± 0.03 | −0.57 ± 0.03 |

**Table 3.**Standardized multiple regression coefficients for the May to August (MJJA) growing season merge of 2466 months. For coefficients: plain text represents p < 0.01 (>99%); italic represents 0.01 ≤ p < 0.05, and coefficients are omitted for p > 0.05.

Variable | A (δOPAQ_{m}) | B (δPR0) | C (δPR1) | D (δPR2) | E (δPR3) | R^{2} |
---|---|---|---|---|---|---|

δT_{x} | −0.95 ± 0.02 | −0.07 ± 0.02 | −0.16 ± 0.02 | 0.58 | ||

δT_{m} | −0.67 ± 0.02 | 0.03 ± 0.02 | −0.10 ± 0.02 | 0.43 | ||

δT_{n} | −0.34 ± 0.02 | 0.18 ± 0.02 | 0.04 ± 0.02 | 0.13 | ||

δDTR | −0.61 ± 0.01 | −0.26 ± 0.01 | −0.15 ± 0.01 | −0.05 ± 0.01 | −0.03 ± 0.01 | 0.73 |

δRH_{n} | 0.59 ± 0.01 | 0.37 ± 0.01 | 0.23 ± 0.01 | 0.09 ± 0.01 | 0.03 ± 0.01 | 0.69 |

δRH_{m} | 0.53 ± 0.01 | 0.32 ± 0.01 | 0.24 ± 0.01 | 0.11 ± 0.01 | 0.04 ± 0.01 | 0.61 |

δRH_{x} | 0.38 ± 0.02 | 0.20 ± 0.02 | 0.20 ± 0.01 | 0.10 ± 0.01 | 0.04 ± 0.01 | 0.36 |

δDRH | −0.22 ± 0.01 | −0.18 ± 0.01 | −0.03 ± 0.01 | 0.26 | ||

δP_{LCLx} | −0.76 ± 0.02 | −0.42 ± 0.02 | −0.31 ± 0.01 | −0.13 ± 0.01 | −0.05 ± 0.01 | 0.68 |

δP_{LCLm} | −0.55 ± 0.01 | −0.30 ± 0.01 | −0.25 ± 0.01 | −0.12 ± 0.01 | −0.04 ± 0.01 | 0.62 |

δP_{LCLn} | −0.30 ± 0.01 | −0.15 ± 0.01 | −0.16 ± 0.01 | −0.08 ± 0.01 | −0.03 ± 0.01 | 0.36 |

δDP_{LCL} | −0.46 ± 0.01 | −0.27 ± 0.01 | −0.15 ± 0.01 | −0.05 ± 0.01 | 0.58 | |

δθ_{Ex} | −0.55 ± 0.02 | 0.28 ± 0.02 | 0.08 ± 0.02 | 0.12 ± 0.02 | 0.21 | |

δθ_{Em} | −0.42 ± 0.02 | 0.30 ± 0.02 | 0.09 ± 0.02 | 0.11 ± 0.02 | 0.17 | |

δθ_{En} | −0.22 ± 0.02 | 0.34 ± 0.02 | 0.09 ± 0.02 | 0.11 ± 0.02 | 0.13 | |

δDθ_{E} | −0.32 ± 0.01 | −0.06 ± 0.01 | 0.37 | |||

δQ_{m} | −0.06 ± 0.02 | 0.41 ± 0.02 | 0.22 ± 0.02 | 0.16 ± 0.02 | 0.22 |

**Table 4.**Surface and TOA fluxes for the MJJA warm season from ERA-Interim for 1979–2013, stratified by ECA, derived from the gridpoints for Estevan, Regina, Saskatoon, and Prince Albert, SK. Mean data in bold are shown in Figure 11.

ECA | K | TOA SW_{dn} | TOA SW_{n} | Surf SWCS_{dn} | Surf SW_{dn} | SWCF | Surf SW_{up} | Surf SW_{n} | Surf Albedo | TOA LW_{up} | Surf LWup | Surf LW_{dn} | Surf LW_{n} |

0.146 | 11 | 427 | 326 | 327 | 279 | −48 | −54 | 225 | 0.19 | −257 | −412 | 328 | −84 |

0.178 | 34 | 427 | 320 | 325 | 268 | −58 | −49 | 218 | 0.18 | −252 | −406 | 329 | −77 |

0.203 | 47 | 426 | 315 | 324 | 258 | −66 | −45 | 213 | 0.17 | −250 | −400 | 327 | −74 |

0.230 | 32 | 424 | 310 | 322 | 248 | −74 | −40 | 208 | 0.16 | −247 | −396 | 326 | −69 |

0.278 | 16 | 427 | 299 | 323 | 233 | −90 | −38 | 195 | 0.16 | −242 | −389 | 325 | −64 |

0.207 | 140 | 426 | 314 | 324 | 257 | −67 | −45 | 212 | 0.17 | −249 | −400 | 327 | −73 |

ECA | K | R_{n} | SH | LH | BR | G | PRECIP | ET | Runoff | T_{x} | T_{m} | T_{n} | DTR |

0.146 | 11 | 141.6 | −53.2 | −71.8 | 0.78 | 16.7 | 1.13 | −2.48 | 0.07 | 24.4 | 18.5 | 12.1 | 12.3 |

0.178 | 34 | 141.4 | −46.1 | −77.4 | 0.62 | 17.9 | 1.69 | −2.67 | 0.04 | 23.0 | 17.4 | 11.2 | 11.8 |

0.203 | 47 | 139.6 | −41.1 | −81.5 | 0.53 | 17.0 | 1.91 | −2.82 | 0.06 | 22.0 | 16.5 | 10.5 | 11.5 |

0.230 | 32 | 138.3 | −33.3 | −88.9 | 0.39 | 16.1 | 2.18 | −3.07 | 0.13 | 21.0 | 15.8 | 10.1 | 11.0 |

0.278 | 16 | 130.8 | −30.9 | −84.5 | 0.37 | 15.4 | 2.92 | −2.92 | 0.13 | 19.4 | 14.5 | 9.2 | 10.3 |

0.207 | 140 | 138.9 | −40.3 | −81.8 | 0.52 | 16.8 | 1.97 | −2.83 | 0.08 | 21.9 | 16.5 | 10.6 | 11.4 |

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**MDPI and ACS Style**

Betts, A.K.; Desjardins, R.L. Understanding Land–Atmosphere–Climate Coupling from the Canadian Prairie Dataset. *Environments* **2018**, *5*, 129.
https://doi.org/10.3390/environments5120129

**AMA Style**

Betts AK, Desjardins RL. Understanding Land–Atmosphere–Climate Coupling from the Canadian Prairie Dataset. *Environments*. 2018; 5(12):129.
https://doi.org/10.3390/environments5120129

**Chicago/Turabian Style**

Betts, Alan K., and Raymond L. Desjardins. 2018. "Understanding Land–Atmosphere–Climate Coupling from the Canadian Prairie Dataset" *Environments* 5, no. 12: 129.
https://doi.org/10.3390/environments5120129